13ｨｪｨ 0002ｨｪｨ 00ｨｦ0602ｨｮ ｨｰｨ ｨｲ07 ﾂｨ 06ｨｦ02, ISSN ﾁ

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13ｨｪｨ 0002ｨｪｨ 00ｨｦ0602ｨｮ050702 0709ｨｰｨ ｨｲ07 ﾂｨ 06ｨｦ02, ISSN 1992-6138 08030607030207070307090303 07030209020703 ﾁ 03000009070807 010908030109080707030709030503 030006090303 ﾁ09020705 0107090708020709 04060303090809 060909070203-04060307 ﾁ0308070803000107090708 09000900 罟ｬ03010302030703 ﾁ1 7" www.lomonosovclub.com ｨｦ03020908030001 07 09070603020708030001: 03030202 010908030109080707030709030503 030006090303 ﾁ09020705 07 04060307 ﾁ030603020705 117419 ｨｪ030709 ﾁ09, 0900. 01030207090905, 02. 37 040009 ﾁ020208 0603020909080306 ｨｦ010908090702 ﾂ.ｨｪ. ｨｰ0302090901070302020905 0903000003050705 090302020900 ｨ.ｨｦ. 01090003 ﾁ0701090905 06. ﾂ. (0308 ﾁ03080708 ﾁ0302020208 070309060308090601) 01090003 ﾁ0701090708 ｨ. ﾂ. 050902030001-09030003 ﾁ ｨ.09. 050301090603 ﾁ ｨｮ.ｨｦ. 0503020708090208070203 ﾁ 06.06. 0503070803020903 ｨｦ.08. ｨｮ0900000702 ｨ.ｨｦ. 6 5 1 (73), 2015 05. c ｨｪ09080301090807070307090303 030006090303 ﾁ09020703", 0703070809 ﾁ0003020703, 2015 05. 03030202 010908030109080707030709030503 030006090303 ﾁ09020705 07 04060307 ﾁ030603020705, ｨｪ030709 ﾁ09, 2015 05. ｨｪ09080301090807070307090303 030006090303 ﾁ09020703", 04030607030207070307090303 07030209020703. ｨｲ0906030507070806070603 ﾁ090203 ﾁ ｨｰ0307090301040307090807 ｨｰ03, 0007010302030705 6 5 015955 0308 15.04.97. 080302040707090203 09 040307090807 31.03.2015 05. 050301040108080306020208 0209000306 07 ﾁ030607080909, 090301040108080306020905 05060904070909: ｨｮ. 050900030403 ﾁ. ｨｹ09070403020708030602: 0109 ﾁ020203 ﾁ 01.ｨ., 0206010704090702 ｨｦ.ｨ., ｨｦ070803010702 01.06. 07080403070908090203 ﾁ 08070403050609040707 ｨ 09090203010707 ﾁ020304020308 0803060503 ﾁ0007, 05. ｨｪ030709 ﾁ09, 0900. 08090203 ﾁ09070209, 02.4. 0700080301 5 04.00. 0007060900 1000 050903. 00030209 07 ﾁ03000302020905.

13ｨｪ09080301090807070307090303 030006090303 ﾁ09020703 020906020900 0303020209 010908030109080707030709030503 030006090303 ﾁ09020705 07 04060307 ﾁ030603020705 6 5 3 (73), 0502 ﾁ090601 { 01090608 2015 05. ｨｮ030203060009020703 0107090607010705 07 0907070803000501 07060302020308 0409030002 ｨ. ｨｰ. ｨｰ0503090203 ﾁ07090708. ｨｪ020305030700030202 07 0302020701 02030703 ﾁ030708020201 2 02. ｨｲ. ｨｮ09 ﾁ03060103 ﾁ09. 000607050302030103080607070307090703 01020305030700030202 12 ｨ. ｨ. ｨｹ ﾁ020702. ｨｪ03080302 01090707 ﾁ 03090209070906 27 ｨｮ0809020302080901 07 04060304030209 ﾁ090803000501 0109080301090807070307090706 0704030107090001020307080308 ﾂ. ﾂ. ｨｦ ﾁ0003 ﾁ. 0700 0302020301 04060302070809 ﾁ0003020707 ﾁ020003060307020206 06090704060302030003020708 48 02. 06. 0803080603 ﾁ09, ｨｮ. ｨ. 080706030503 ﾁ. ｨｰ0903020303 0700030003020703 060903020206 ﾁ030007070702 53 ｨｮ030203060009020703 030006090303 ﾁ09020705: 050303010308060705 05. ｨｬ03030902. 060803 0809090303 ﾁ0309080306? 56 ｨｦ03 07070803060707 010908030109080707030709030503 030006090303 ﾁ09020705 00. ｨｦ. 05090302030103 ﾁ09. 01030003 ｨｦ. 05. ｨ 020206030203 ﾁ09 0007 ﾁ03: ｨｮ03010702090609 縺080306030203 ﾁ0203 07020307 ﾁ 04060304030209 ﾁ09020707 01090803010908070907 ﾁ ｨｰ0307070707 07 0309 060900030003011 7 { 55. 020503 03070203 ﾁ0908030008 ｨｦ. 05. ｨ 020206030203 ﾁ09 { 120 60 ｨｦ020403060109010705 0708 0603020909010707. 07 ﾁ0206030203 0902070507 ｨｲ090509020909 01090502070809" 77

130107090607010705 07 0907070803000501 07060302020308 0409030002 ｨｪ020305030700030202 07 0302020701 02030703 ﾁ030708020201 ｨ. ｨｰ. ｨｰ0503090203 ﾁ07090708 08060302000905090301 ﾁ02070109020708 070708090803000308 070809080108 03 0102030503070003020906 07 0302020308 04030603010302020308, 020307080904020908 0907090607010705 04060304070001020206 040703070903-0109080301090807070307090706 090009070703 ﾁ. ｨ ﾁ080306 07070403000103090308 05080308 0109080306070900 090909 08030306030807070307090703 07 ﾁ030203020705 07020907090009 ﾁ 8-06 0109080301090807070307090706 09000907070906 1 (030302090903010003020703), 0309080301 ﾁ 10-06 09000907070906 090909 0309090603040003020703 080301, 070309070302020206 0609020303. 01030807 0709010307080305080300010203 07030907090808 02090407070902020208 0803090708, 09 0309080301 09070708030001 0308 ﾁ0307090308 0209 0706 ﾁ030406030702. 0506030103 0508030503, 030207 ﾁ0204030002050808 07040301070900010203 06090306090003080902020203 020005 020706 040609090807070307090703 03090209020705. ｨｦ0309070903010208 090709060701070705 0803090708 07040301070900010203 090209-0408070603 ﾁ0902 020005 0706 ﾁ03030609070809. ﾂ 10-01 090009070703 0803090708 0103000308 00020801 040607000007000302 09 010908030109080707030709030109, 03070007 090603 ﾁ030201 09070302070903 ﾁ 090009070709 040303 ﾁ0300050308 ﾁ ﾁ03070807 0900070806090908020303 04030205080703 090005030006090707030709030503 090300010109. ｨｮ0809080105 04030709080903080705 07 040603020300000302070301. 1. 08060307080308040703 04030205080705 ｨｪ02030503070003020301 07080304030207 n 0308 030202030503 02030703 ﾁ03070802030503 x 02090302 ﾁ0903080705 ﾁ0206090003020703 ﾁ070209 p(x) = a n x n + a n6ﾓ11 x n6ﾓ11 + + a 1 x + a 0 ; (1) 050203 0203080708 ﾁ0708030001020203 0707070009 a n ; a n6ﾓ11 ; : : : ; a 1 ; a 0 090305040407010703020802 01020305030700030209, 040607070501 a n ﾙ 0, 09 030708090001020203 05 ﾁ000508080705 0406030703 ﾁ03000102020107 07070700090107; n 0103000303 020303080607010908030001020303 0707070003. 0503050404070107030208 a n 02090302 ﾁ0903080705 07080906040701 09030504040701070302080301 01020305030700030209; 0903050404070107030208 a 0 07 ﾁ03000302020201 070003020301 01020305030700030209; 0707070003 n 0708030403020108 01020305030700030209, 040607 05080301 0407040908 deg p(x) = n; 0302020307000302 a n x n 07080906040701 070003020301 01020305030700030209. 0609040607010306, p(x) = 6x 5 6ﾓ15x 3 +1;2x 2 +x6ﾓ112 03070801 010203050307000302 (070007 0103000905 060901070302090001020905 04090209010705) 0405080308 07080304030207 0308 x 07 0903050404070107030208090107 a 5 = 6, a 4 = 0, a 3 = 6ﾓ15, a 2 = 1, a 0 = 6ﾓ112. 0708000707020303 0308 02090005 0707070003 05 ﾁ000503080705 0102030503070003020301 02090003 ﾁ0308 07080304030207. 0607070003 0 05 ﾁ000503080705 0102030503070003-020301, 020005 0903080306030503 07080304030201 0203 030406030203000503080705. 07080103080701, 070803 01020305030700030202 0308 030202030503 02030703 ﾁ03070802030503 070203050209 02090302 ﾁ090808 010203050307000302090107 07 0302020308 04030603010302020308. ｨｲ0904070701 01020305030700030209 ﾁ 0403060103 (1) 02090302 ﾁ0903080705 0708090202090608020201 ﾁ07020301 01020305030700030209. ﾂ 05080308 030904070707 0209 040306 ﾁ0301 0103070803 020906030207080705 07080906040708 07000302 01020305030700030209, 09 030708090001020203 0700030202 0609070403000300030202 0403 090002- ﾁ0908060701 0708030403020501 02030703 ﾁ03070802030503. ｨｦ0203050209 0708090202090608020201 ﾁ07020301 01020305030700030209 02090302 ﾁ090808 0809090908 030503 030904070701, ﾁ 09030803060308 0209 040306 ﾁ0301 0103070803 020906030207080705 07 ﾁ03000302020208 07000302, 09 030708090001020203 0700030202 0609070403000300030202 0403 ﾁ0303060907080908060701 0708030403020501 02030703 ﾁ03070802030503: p(x) = a 0 + a 1 x + + a n6ﾓ11 x n6ﾓ11 + a n x n (2) ｨｹ0807 030904070707 (1) 07 (2) 0701030808 07030308 ﾁ03080708 ﾁ0908060703 020903 ﾁ09020705: 030904070701 0403 ﾁ0303060907080908060701 0708030403020501 07 030904070701 0403 090002 ﾁ0908060701 0708030403020501 02030703 ﾁ03070802030503. 0809070801, 0209040607010306, 020902 010203050307000302 p(x) = 1 + 2x 6ﾓ1 7x 3 + x 4. ｨｲ090103020701 ﾁ 05080301 0609 ﾁ03020708 ﾁ03 ﾁ07080209 02030703 ﾁ030708020303 06 070707000301 2. 08030009070701 p(2) = 1 + 2 2 6ﾓ1 7 2 3 + 2 4 = 6ﾓ135. 08030009070302020303 0707070003 6ﾓ135 02090302 ﾁ0903080705 030209070302070301 01020305030700030209 ﾁ 0803070903 2. ｨｦ0007, 0209040607010306, 020005 01020305030700030209 (2) 0302090703020703 p(1) = a 0 + a 1 + + a n6ﾓ11 + a n 0609 ﾁ0203 0709010103 ﾁ070306 030503 090305040407010703020803 ﾁ. 01 ﾁ09 01020305030700030209 p(x) 07 q(x) 0308 030202030503 02030703 ﾁ03070802030503 02090302 ﾁ0908080705 0609 ﾁ02020107 (08030002030708 ﾁ03020203 0609 ﾁ02020107), 03070007 0706 0302090703020705 040607 0008000206 030209070302070506 02030703 ﾁ03070802030503 03020702090903 ﾁ02, 0803 03070801 0609 ﾁ0202 0103000209 0703000308. 1 0409030002 6 5 179 05. ｨｪ030709 ﾁ02 2

13ｨｪ020305030700030202 07 0302020701 02030703 ﾁ030708020201 3 00030002030708 ﾁ0302020303 0609 ﾁ03020708 ﾁ03 02 ﾁ0906 01020305030700030203 ﾁ 030003030209070903080705 030209090301 ﾔ: p(x) ﾔ q(x). 0609040607010306, 0302090703020705 01020305030700030209 p(x) = 1 + 2x 6ﾓ1 7x 3 + x 4 ﾁ 0803070903 2 0609 ﾁ0203 06(2) = 6ﾓ135 07 0302090703020703 01020305030700030209 q(x) = 6ﾓ145 + 5x ﾁ 0803070903 2, 0803 03070801 q(2) = 6ﾓ145 + 5 2 = 6ﾓ135 03020702090903 ﾁ02, 0203 ﾁ 0803070903 0 0701030301 p(0) = 1 + 2 0 6ﾓ1 7 0 3 + 0 4 = 1, 09 q(0) = 6ﾓ145 + 5 0 = 6ﾓ145, 0803 03070801 01020305030700030202 p(x) = 1+2x6ﾓ17x 3 +x 4 07 q(x) = 6ﾓ145+5x 08030002030708 ﾁ03020203 0203 0609 ﾁ0202. ｨｪ02 0103000301 0209040707090801p(x) 6ﾘ7 q(x). 00030306030109. 01 ﾁ09 01020305030700030209 p(x) 07 q(x) 0308 0302020308 04030603010302020308 0609 ﾁ0202 0803050209 07 080300010903 0803050209, 0903050209 0706 1)07080304030207 0609 ﾁ0202 07 2)090305040407010703020802 040607 03020702090903 ﾁ0206 0708030403020506 02030703 ﾁ03070802030503 03020702090903 ﾁ02. 010005 020309090309080300010708 ﾁ09 08030306030102 0406070103020701 070003020908060303 ﾁ0704030103050908030001020303 0908 ﾁ0306000203020703: 03070007 010203-050307000302 08030002030708 ﾁ03020203 0609 ﾁ0302 02090008, 0803 ﾁ0703 030503 090305040407010703020802 0609 ﾁ0202 02090008 (0203090900070803 030503 07090103-07080305080300010203). 010309090309080300010708 ﾁ03. 0809070801 p(x) ﾔ q(x) 07 p(x) = a 0 + a 1 x + + a n6ﾓ11 x n6ﾓ11 + a n x n ; a n ﾙ 0; q(x) = b 0 +b 1 x + +b m6ﾓ11 x m6ﾓ11 +b m x m ; b m ﾙ 0; 07 0406030204030003000701, 070803 n < m. ｨｲ090407040301 08030002030708 ﾁ03 a 0 + a 1 x + + a n6ﾓ11 x n6ﾓ11 + a n x n ﾔ b 0 + b 1 x + + b m6ﾓ11 x m6ﾓ11 + b m x m 07 04030003000701 ﾁ 020501 x = 0 (0102 0701030301 040609 ﾁ03 ﾁ020006090801 0008000303 0302090703020703 04030603010302020308). 08030009070701 a 0 + a 1 0 + + a n6ﾓ11 0 n6ﾓ11 + a n 0 n = b 0 + b 1 0 + + b m6ﾓ11 0 m6ﾓ11 + b m 0 m : 070807080209 04030009070701 a 0 = b 0. 000304030601 0609 ﾁ03020708 ﾁ03 (6ﾓ5) 040607020701090308 ﾁ0702 a 0 + a 1 x + + a n6ﾓ11 x n6ﾓ11 + a n x n ﾔ 09 0 + b 1 x + + b m6ﾓ11 x m6ﾓ11 + b m x m : (6ﾓ5) 070807080209 a 1 x + + a n6ﾓ11 x n6ﾓ11 + a n x n ﾔ b 1 x + + b m6ﾓ11 x m6ﾓ11 + b m x m 07, 02030005 030003 0709070807 0403000907030202030503 0609 ﾁ03020708 ﾁ09 0209 06, 0403000907090301 a 1 + + a n6ﾓ11 x n6ﾓ12 + a n x n6ﾓ11 ﾔ b 1 + + b m6ﾓ11 x m6ﾓ12 + b m x m6ﾓ11 : (6ﾓ56ﾓ5) ｨｦ03 (6ﾓ56ﾓ5) 09020900030507070203 020908020501, 070803 a 1 = b 1. 02070007 0009020301 040307080904090801 09020900030507070203, 0803 04030700030203 ﾁ09080300010203 04030009070701 0107070802 ﾁ0905 050807 0609 ﾁ03020708 ﾁ09, 0703 (6ﾓ5) 0403000907090301 a 2 = b 2 ; a 3 = b 3 ; a 4 = b 4 ; : : : ; a m = b m : a 0 + a 1 x + + a n6ﾓ11 x n6ﾓ11 + a n x n ﾔ a 0 + a 1 x + + a n6ﾓ11 x n6ﾓ11 + a n x n + b n+1 x n+1 + + b m x m ; 030809090209 0003050209 0 ﾔ b n+1 x n+1 + + b m x m : 0 ﾔ x n+1 (b n+1 + +b m x m6ﾓ1n6ﾓ11 ) 6ﾍ2 0 ﾔ b n+1 +b n+2 x +b m x m6ﾓ1n6ﾓ11 6ﾍ2 b n+1 = b n+2 = = b m = 0 (?!) 0803000907070007 0406030807 ﾁ030603070703. ｨｲ0209070708, 02030609 ﾁ03020708 ﾁ03 n < m 0203 ﾁ03060203. ｨ 020900030507070203, 0203 ﾁ03060203 07 n > m. ｨｮ00030203 ﾁ09080300010203, n = m, 0803 03070801 07080304030207 08030002030708 ﾁ03020203 0609 ﾁ020206 01020305030700030203 ﾁ 0609 ﾁ0202 07, 0700030203 ﾁ09-080300010203, 0403 ﾁ0803060505 0609070709000203020705 020005 070009070905 n = m, 020908020501, 070803 a 0 = b 0, a 1 = b 1, a 2 = b 2,... ; a n = b n, 0803 03070801 090305040407010703020802 08030002030708 ﾁ03020203 0609 ﾁ020206 01020305030700030203 ﾁ 040607 03020702090903 ﾁ0206 0708030403020506 02030703 ﾁ03070802030503 0609 ﾁ0202, 07.08.02.

134 ｨ. ｨｰ. ｨｰ0503090203 ﾁ07090708 080607010306. 0609080807 0707070009 A, B 07 C, 03070007 0703 ﾁ0307080203, 070803 01020305030700030202 p(x) = A(x 2 + x + 1) + (Bx + C)(x + 1) 07 q(x) = x 2 + 3x + 2 0609 ﾁ0202 040607 0008000206 030209070302070506 x. ｨｰ030403020703. 1 070403070300. ｨｲ090407040301 010203050307000302 p(x) ﾁ 0708090202090608020301 ﾁ070203 0403 090002 ﾁ0908060701 0708030403020501 x. 010005 0508030503 0609070906030301 070903000907 07 040607 ﾁ03020501 0403020300020203 0700030202. ﾂ 06030309000108090803 04030009070701 0803 09070003 ﾁ0708 p(x) ﾔ q(x). ｨｲ0209070708, p(x) = (A + B)x 2 + (A + B + C)x + (A + C): (A + B)x 2 + (A + B + C)x + (A + C) ﾔ x 2 + 3x + 2: 070807080209 07000302090308, 070803 090305040407010703020802 01020305030700030203 ﾁ p(x) 07 q(x) 040607 03020702090903 ﾁ0206 0708030403020506 x 0609 ﾁ0202. 0803000907090301 07070708030109 090609 ﾁ0203020708 61 62 A + B = 1; A + B + C = 3; 63 A + C = 2: 02070007 ﾁ03 ﾁ0803060301 090609 ﾁ0203020707 090703070801 040306 ﾁ0303 0609 ﾁ03020708 ﾁ03, 0803 020908020501 C = 2. 000304030601 0703 0806030801030503 090609 ﾁ0203020705 02090603020701 A = 0. 06090903020301, 0703 040306 ﾁ030503 090609 ﾁ0203020705 0403000907090301 B = 1. ｨｦ080909, A = 0, B = 1, C = 2. 2 070403070300. 080307090300010909 0403 09070003 ﾁ0708 p(x) ﾔ q(x), 0803 0706 0609 ﾁ03020708 ﾁ03 0703000008020903080705 040607 0008000206 030209070302070506 06. ｨｲ090407040301 0609 ﾁ03020708 ﾁ03 p(x) = q(x) ﾁ 080307090906 x = 6ﾓ11; x = 0; x = 1. ﾂ 06030309000108090803 04030009070701 x A(x 2 + x + 1) + (Bx + C)(x + 1) ﾔ x 2 + 3x + 2 6ﾓ11 A((6ﾓ11) 2 + (6ﾓ11) + 1) + (B(6ﾓ11) + C)((6ﾓ11) + 1) = (6ﾓ11) 2 + 3(6ﾓ11) + 2 0 A(0 2 + 0 + 1) + (B 0 + C)(0 + 1) = 0 2 + 3 0 + 2 1 A(1 2 + 1 + 1) + (B 1 + C)(1 + 1) = 1 2 + 3 1 + 2 010005 02090603000203020705 07070903010206 0707070300 A, B 07 C 0403000907070007 07070708030109 08060506 090609 ﾁ0203020708 07 0806030105 02030703 ﾁ030708-02020107: 61 62 A = 0; A + C = 2; 63 3A + (B + C) 2 = 6: ｨｰ03040302070301 07070708030102 05 ﾁ000503080705 0209000306 0703 08060506 0707070300 A = 0; B = 1; C = 2. 0803000907070007 080308 0003 0709010208 060303090001080908. 07080103080701, 070803 ﾁ0803060308 070403070300 06030403020705 07070403000103090308 070003020908060708 ﾁ0900020208 04090908: 01 ﾁ09 01020305030700030209 07080304030207 n ﾝ 0 08030002030708 ﾁ03020203 0609 ﾁ0202 0803050209 07 080300010903 0803050209, 0903050209 0706 0302090703020705 0703 ﾁ040902090808 ﾁ n + 1 080307090906. 01060905070107 070003 ﾁ090107, 0703060303 n+1 0803070909 090303060207020908020308 040003070903070807 (07 04030409060203 06090300070702020107 090007010707-07090107) 0406030603020708 050609040709 030207020708 ﾁ030202030503 01020305030700030209 07080304030207 n. 2. ｨｮ00030003020703 07 ﾁ0207070809020703 01020305030700030203 ﾁ ｨｮ0901010308 02 ﾁ0906 01020305030700030203 ﾁ 02090302 ﾁ0903080705 010203050307000302, 04030009070302020208 070003000302070301 ﾁ070306 030202030700030203 ﾁ, ﾁ06030205060706 ﾁ 050807 01020305030700030202. ｨｮ080304030201 0709010102 01020305030700030203 ﾁ 0203 ﾁ020403 00030001040308 0703 0708030403020308 0102030503-0700030203 ﾁ-070009050903010206. 0609040607010306, (x 3 + 6x 6ﾓ1 2) + (6ﾓ1x 3 6ﾓ1 2x 2 + x + 7) = 6ﾓ12x 2 + 7x + 5: ﾂ 07090708020301 070009070903, 0903050209 090305040407010703020802 01020305030700030203 ﾁ 0406030807 ﾁ0304030003000202, 0706 0709010109 08030002030708 ﾁ03020203 0609 ﾁ0209 02090008: (4x 6ﾓ1 2) + (6ﾓ14x + 2) ﾔ 0.

13ｨｪ020305030700030202 07 0302020701 02030703 ﾁ030708020201 5 ｨｰ0303090001080908 ﾁ0207070809020705 02 ﾁ0906 01020305030700030203 ﾁ 02090302 ﾁ0903080705 0706 060903020307080108. ｨｰ09030203070801 02 ﾁ0906 0102030503070003-0203 ﾁ p(x) 07 q(x) 030406030203000503080705 070003020908060701 0609 ﾁ03020708 ﾁ0301: p(x) 6ﾓ1 q(x) = p(x) + (6ﾓ11) q(x): 080607 05080301 p(x) 02090302 ﾁ0903080705 0102030503070003020301-0901030201040903010201, q(x) 0102030503070003020301- ﾁ020707080903010201. 07080103080701, 070803 0700030003020703 07 ﾁ0207070809020703 01020305030700030203 ﾁ 0103000203 ﾁ0204030002050801 縺0708030000070903011 7 04030203000203 0700030003020708 07 ﾁ0207070809020708 0103000206 0707070300. ｨｲ090407070902020203 縺0708030000070903011 7 01020305030700030202 020300000202 00020801 0609070403-000300030202 0403 090002 ﾁ0908060701 (070007 0403 ﾁ0303060907080908060701) 0708030403020501 02030703 ﾁ03070802030503, 040607070501 ﾁ 05080308 030904070707 020300000202 0406070709080708 ﾁ03 ﾁ090801 ﾁ0703 090305040407010703020802 01020305030700030203 ﾁ, ﾁ090008070905 02090003 ﾁ0203. 0609040607010306, 0409070801 030902090202 01020305030700030202 p(x) = 3x 4 + x 2 6ﾓ1 6x + 2 07 q(x) = 2x 4 6ﾓ1 3x 3 + 5x 2 6ﾓ1 12x 6ﾓ1 5: ｨｰ090707010308060701 04060701030602 0700030003020705 07 ﾁ0207070809020705 01020305030700030203 ﾁ 縺0708030000070903011 7: 1) 3x 4 + 0x 3 + 1x 2 6ﾓ1 6x + 2 + 2x 4 6ﾓ1 3x 3 + 5x 2 6ﾓ1 12x 6ﾓ1 5 5x 4 6ﾓ1 3x 3 + 6x 2 6ﾓ1 18x 6ﾓ1 3 2) 3x 4 + 0x 3 + 1x 2 6ﾓ1 6x + 2 6ﾓ1 2x 4 6ﾓ1 3x 3 + 5x 2 6ﾓ1 12x 6ﾓ1 5 x 4 + 3x 3 6ﾓ1 4x 2 + 6x + 7 080607 0700030003020707 ( ﾁ0207070809020707) 02 ﾁ0906 01020305030700030203 ﾁ, 0903050209 070003000203 04030603040908090801 0403020300020203 030202030700030202 01020305030700030203 ﾁ, 0706 0103000203 030904070702 ﾁ090801 0003000303 090609080903, 03040907090905 030202030700030202 07 02090003 ﾁ020107 09030504040701070302-08090107. 0609040607010306: 3) x 5 6ﾓ1 x 4 + x 6ﾓ1 5 + x 4 6ﾓ1 x 2 + x + 6 x 5 6ﾓ1 x 2 + 2x + 1 4) x 5 6ﾓ1 x 4 + x 6ﾓ1 5 6ﾓ1 x 4 6ﾓ1 x 2 + x + 6 x 5 6ﾓ1 2x 4 + x 2 6ﾓ1 11 080607 0809090308 縺000307040306050203070203081 7 0403060103 030904070707 01020305030700030203 ﾁ 020005 0706 0700030003020705 07 ﾁ0207070809020705 0806030009-03080705 0403 ﾁ02040302020303 ﾁ02070109020703. 3. 010102030003020703 01020305030700030203 ﾁ 0806030703 ﾁ03020302070301 02 ﾁ0906 01020305030700030203 ﾁ 02090302 ﾁ0903080705 010203050307000302, 0609 ﾁ020208 0709010103 0406030703 ﾁ030203020708 0909000203-0503 030202030700030209 030202030503 01020305030700030209 0209 090900020208 0703 030202030700030203 ﾁ 02060905030503 01020305030700030209. 01060905070107 070003 ﾁ090107, 040607 090102030003020707 01020305030700030203 ﾁ 070704030001030903080705 0609070406030203000708030001020208 0309090302 09010203-0003020705 030802030707080300010203 0700030003020705. 0609040607010306, (x 3 6ﾓ1 1)(x 3 + 2x + 1) = x 6 + 2x 4 + x 3 6ﾓ1 x 3 6ﾓ1 2x 6ﾓ1 1 = x 6 + 2x 4 6ﾓ1 2x 6ﾓ1 1: ｨｮ080304030201 0406030703 ﾁ030203020705 01020305030700030203 ﾁ 0609 ﾁ0209 0709010103 0708030403020308 01020305030700030203 ﾁ-070301020300070803000308. 01 ﾁ09 01020305030700030209 0103000203 0901020300090801 縺0708030000070903011 7, 04030204070702 ﾁ0905 01020305030700030202-0703010203000708030007 03020702 040302 020609050701, 04030203000203 08030109, 090909 0901020300090808 0103000203 0707070009, 040607070501 0209070702090808 0901020300090801 0703 0708090604030503 0700030209 010203000708030005. 080607 0809090301 07040307030003 090102030003020705 09020300020303 040607 ﾁ0302070801 0403020300020203 0700030202. 0609040607010306, x 4 + 0 x 3 + 0 x 2 + 2x + 1 ﾁ x 2 6ﾓ1 3x + 2 x 6 + 0 x 5 + 0x 4 + 2x 3 + x 2 + 6ﾓ1 3x 5 + 0x 4 + 0x 3 6ﾓ1 6x 2 6ﾓ1 3x 2x 4 + 0x 3 + 0x 2 + 4x + 2 x 6 6ﾓ1 3x 5 + 2x 4 + 2x 3 6ﾓ1 5x 2 + x + 2 05030203070203, 090909030902020208 070403070300 05060301030302090708, 0203 070203050209 030503 04060701030203020703 0309090302 ﾁ0903080705 0403000303020201.

136 ｨ. ｨｰ. ｨｰ0503090203 ﾁ07090708 4. 01030003020703 01020305030700030203 ﾁ 0809070801 p(x) 07 q(x) 02 ﾁ09 0406030703 ﾁ030001020206 01020305030700030209. ｨｪ0203050307000302 p(x) 02030007080705 0209 010203050307000302 q(x)0803050209 07 080300010903 0803050209, 0903050209 070906030708 ﾁ090308 0809090308 010203050307000302 t(x), 070803 040607 0008000206 030209070302070506 04030603010302020308 x ﾁ02040300020503080705 0609 ﾁ03020708 ﾁ03 p(x) = q(x) t(x). ﾂ 05080301 070009070903 010203050307000302 t(x) 02090302 ﾁ0903080705 07090708020201 0308 02030003020705 p(x) 0209 q(x). ｨｪ0203050307000302 q(x) 02090302 ﾁ0903080705 020300070803000301 01020305030700030209 p(x), 09 010203050307000302 p(x) 02030007010201. 02070007 p(x) 02030007080705 0209 q(x), 0803 0407040908 p(x).q(x). 080607 05080301, ﾁ 07070009 040609 ﾁ070009 090102030003020705 01020305030700030203 ﾁ, 07080304030201 0709070802030503 t(x) 0609 ﾁ0209 0609030203070807 0708030403020308 0203000701030503 07 0203000708030005: p n (x) = q m (x) t n6ﾓ1m(x), 040607070501 n 6ﾓ1 m ﾝ 0. 070807080209 07000302090308, 070803 03070007 p(x) 02030007080705 0209 q(x), 0803 07080304030201 p(x) 0203 010302010403 07080304030207 q(x). 0609040607010306, 010203050307000302 p(x) = x 3 6ﾓ11 02030007080705 0209 010203050307000302 q(x) = x 2 +x+1, 080909 090909 0609 ﾁ03020708 ﾁ03 x 3 6ﾓ1 1 = (x 2 + x + 1)(x 6ﾓ1 1) ﾁ02040300020503080705 040607 0008000301 x. ｨｮ 020609050308 07080306030202, 010203050307000302 p(x) = 5x + 6 0203 02030007080705 0209 010203050307000302 q(x) = 2x 2 + 1, 080909 090909 07080304030201 p(x) 010302010403 07080304030207 q(x). ｨｪ02 ﾁ07020701, 070803 02030003020703 01020305030700030203 ﾁ 0203 ﾁ0703050209 ﾁ03030103000203. ﾂ0900020303 030901030709020703. 07080103080701 ﾁ0900020208 07090708020208 070009070908 02030003020705 01020305030700030209 p(x) 07080304030207 n, n ﾝ 0, 0209 010203050307000302 q(x) = c, c ﾙ 0 02090003 ﾁ0308 07080304030207, 0803 03070801 0209 0707070003, 0203 0609 ﾁ020303 02090008. 0609040607010306, 03070007 p(x) = 2x 6ﾓ1 5 07 q(x) = 7, p(x).q(x), 040307090300010909 07040609 ﾁ03020007 ﾁ03 0609 ﾁ03020708 ﾁ03 2x 6ﾓ1 5 ﾔ 7 (2 7 x 6ﾓ1 5 7), 0803 03070801 07090708020303 0309020902020206 01020305030700030203 ﾁ 03070801 010203050307000302 2 7 x 6ﾓ1 5 7. ｨｰ090707010308060701, 030605 03020702 040607010306. 0809070801 p(x) = 6ﾓ15 07 q(x) = 7. ﾂ 05080301 070009070903 0304050801 p(x).q(x), 040307090300010909 6ﾓ15 ﾔ 7 (6ﾓ1 5 7). ｨｮ0003000203070801 040607 ﾁ0302050202030503 04060701030609 ﾁ 080301, 070803 090909 0103000203 0707070009 0707070003 (6ﾓ15) 0209 7 0203 02030007080705. 070202090903, 060907070109080607 ﾁ0905 050807 0003 0707070009 090909 01020305030700030202, 0403000907090301, 070803 010203050307000302 (6ﾓ15) 02030007080705 0209 010203050307000302, 0609 ﾁ020208 7, 000303 03070809080909! ｨｪ02 ﾁ07020701, 070803 0008000308 010203050307000302 07080304030207 n, n ﾝ 0, ﾁ0703050209 02030007080705 0209 0008000308 010203050307000302 02090003 ﾁ0308 07080304030207. 5. 01030003020703 01020305030700030203 ﾁ 07 0307080908090301 00030306030109. 010005 0008000206 02 ﾁ0906 01020305030700030203 ﾁ p n (x) 07 q m (x), 050203 q m (x) 0203 0609 ﾁ0302 08030002030708 ﾁ03020203 02090008, 070906030708 ﾁ090808 07 030207020708 ﾁ03020202 01020305030700030202 t n6ﾓ1m(x) 07 r s (x) 0809090703, 070803 020005 ﾁ070306 0302090703020708 x ﾁ02040300020503080705 0609 ﾁ03020708 ﾁ03 p n (x) = q m (x)t n6ﾓ1m(x) + r s (x); (3) 050203 n; m; n 6ﾓ1m; s 07080304030207 07030308 ﾁ03080708 ﾁ0908060706 01020305030700030203 ﾁ, 040607070501 03070007 r s (x) ﾙ 0, 0803 s < m: ｨｪ0203050307000302 r s (x) 02090302 ﾁ0903080705 0307080908090301 0308 02030003020705 p n (x) 0209 q m (x). 02070007 03070809080309 0203 05 ﾁ000503080705 02090003 ﾁ0201 0102030503070003020301, 0803 010203050307000302 t n6ﾓ1m(x) 02090302 ﾁ0903080705 0203040300020201 07090708020201 0308 02030003020705 p n (x) 0209 q m (x). 02070007 0003 r s (x) ﾔ 0, 0803 p n (x).q m (x): 0806030708070803 ﾁ02070109080300010203! 02070007 07080304030201 n 01020305030700030209 p n (x) 0203 010302010403 07080304030207 01020305030700030209 q m (x), 0803 07080304030201 0709070802030503 01020305030700030209 t n6ﾓ1m(x) 0609 ﾁ0209 n 6ﾓ1 m ﾝ 0. 02070007 0003 07080304030201 n 010302010403 07080304030207 m, 0803 0203040300020303 07090708020303 03070801 02090003 ﾁ0308 010203050307000302, 030503 07080304030201 0203 03040603020300030209, 09 03070809080309 r(x) ﾔ p(x). 0609040607010306, 040607 02030003020707 01020305030700030209 5x + 6 0209 2x 2 + 1 07 0307080908090301 04030009070701 0203040300020303 07090708020303, 0609 ﾁ020303 02090008, 07 03070809080309, 0609 ﾁ020208 5x + 6. 020503 07080304030201 0609 ﾁ0209 1 07 030209 010302010403 07080304030207 0203000708030005, 0609 ﾁ020308 2. ｨｰ09 ﾁ03020708 ﾁ03 (3) ﾁ 020902020301 070009070903 0009020308 ﾁ0204030002030203 07 0701030308 ﾁ0702 5x + 6 = (2x 2 + 1) 0 + (5x + 6): 01030003020703 02 ﾁ0906 01020305030700030203 ﾁ 07 0307080908090301 05 ﾁ000503080705 0902090003050301 07030308 ﾁ03080708 ﾁ0908060308 0304030609010707 020902 010300020107 07070700090107.

13ｨｪ020305030700030202 07 0302020701 02030703 ﾁ030708020201 7 02070007 010203050307000302 p n (x) 040607 02030003020707 0209 q m (x) 02090508 03070809080309 r s (x), 0803 040607 02030003020707 p n (x) 0209 010203050307000302 c q m (x); c ﾙ 0, 03070809080309 r s (x)0203 07030103020503080705. ｨｹ0803 0300080507020503080705 070003020908060701 08030002030708 ﾁ0301: p n (x) = (c q m (x)) t n6ﾓ1m(x) c + r s (x) 08030508030109 070203050209 0503 ﾁ03060508, 070803 02030003020703 01020305030700030203 ﾁ 03040603020300030203 07 080307020307080108 0203 04030708030502020308. 6. 01030003020703 01020305030700030203 ﾁ 縺090503000903011 7 01030003020703 01020305030700030203 ﾁ 縺090503000903011 7 03070801 090005030607080107070307090708 070403070300 02090603000203020705 0709070802030503 (070007 020304030002030503 0709070802030503 07 03070809080909), 04030603000708 0209 0103080302 02030003020705 縺090503000903011 7 0209080906090001020206 0707070300 07 0903-020307020206 02030705080707020206 020603000308. 010005 ﾁ020403000203020705 090005030607080109 02030007010303 p(x) 07 0203000708030001 q(x) 030904070702 ﾁ090808 ﾁ 0708090202090608020301 ﾁ070203 0403 090002 ﾁ0908060701 0708030403020501 04030603010302020308 07 0406030703 ﾁ03020508 02030003020703 縺090503000903011 7. 080607010306. ｨｰ0903020300070801 縺090503000903011 7 010203050307000302 p(x) = 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 0209 010203050307000302 q(x) = 2x 3 + x 2 + 1. ｨｰ030403020703. I 040905. 06090603020701 040306 ﾁ0208 07000302 0709070802030503. 010005 0508030503 0203000701 07080906040708 07000302 0203000701030503 4x 5 0209 07080906040708 07000302 0203000708030005 2x 3. 0803000907090301 2x 2, 09030803060208 04030204070702 ﾁ090301 040302 020300070803000301: 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 2x 3 + x 2 + 1 2x 2 II 040905. 06090603020701 ﾁ0803060308 07000302 0709070802030503. 010005 0508030503 07020907090009 020908020501 0406030703 ﾁ030203020703 2x 2 07 02030007-08030005, 07 050803 0406030703 ﾁ030203020703 0403020407040301 040302 02030007010201. ｨｲ09080301 04030009070302020303 0406030703 ﾁ030203020703 ﾁ02070708090301 0703 0203000701030503 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 縺0708030000070903011 7 (040607 05080301 04030204070702 ﾁ090801 02060905 040302 020609050301 0403020300020203 030202030700030202 02030300050309080300010203). ｨｹ0809 0609030203070801 03070801 040306 ﾁ0208 03070809080309: 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 2x 3 + x 2 + 1 4x 5 + 2x 4 + 2x 2 2x 2 040306 ﾁ0208 03070809080309: 6ﾓ12x 4 6ﾓ1 2x 3 6ﾓ1 3x 2 + x + 1 ﾂ 06030309000108090803 0102 罍ﾁ03060209000707011 7 09 I 04090509, 080909 090909 07010308080705 02 ﾁ09 01020305030700030209, 06090704030003000302020203 0403 090002 ﾁ0908060701 0708030403020501 x. ｨｰ090302030007 ﾁ 07080906040708 07000302 (6ﾓ12x 4 ) 02090802030202030503 01020305030700030209 (6ﾓ12x 4 6ﾓ1 2x 3 6ﾓ1 3x 2 + x + 1) 0209 07080906040708 07000302 2x 3 0203000708030005, 04030009070701 ﾁ0803060308 07000302 0709070802030503: 6ﾓ1x. 020503 030904070702 ﾁ090301 0605020301 07 020908020302020201 0609020303 040306 ﾁ0201 070003020301: 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 2x 3 + x 2 + 1 4x 5 + 2x 4 + 2x 2 2x 2 6ﾓ1 x 6ﾓ12x 4 6ﾓ1 2x 3 6ﾓ1 3x 2 + x + 1 III 040905. 06090603020701 080603080708 07000302 0709070802030503. 010005 0508030503 0403 ﾁ080306050301 0803 0003 0304030609010707, 09030803060203 00020007 03040707090202 ﾁ03 II 04090503, 09 070103020203: 020908020302020208 ﾁ0803060308 07000302 0709070802030503 (6ﾓ1x) 0901020300090301 0209 0203000708030001 07 04030204070702 ﾁ090301 04030009070302020303 0406030703 ﾁ030203020703 (6ﾓ12x 4 6ﾓ1 x 3 6ﾓ1 x) 040302 040306 ﾁ0201 0307080908090301, 0609 ﾁ020201 6ﾓ12x 4 6ﾓ1 2x 3 6ﾓ13x 2 +x+1. ﾂ020707080905 縺0708030000070903011 7, 02090603020701 ﾁ0803060308 03070809080309 (6ﾓ1x 3 6ﾓ13x 2 +2x+1). ｨｲ09080301 0203000701 07080906040708 07000302 ﾁ080306030503 03070809080909 0209 07080906040708 07000302 0203000708030005. ﾂ 06030309000108090803 0009020308 020908020302 080603080708 07000302 0709070802030503 ({0,5): 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 2x 3 + x 2 + 1 4x 5 + 2x 4 + 2x 2 2x 2 6ﾓ1 x 6ﾓ1 0;5 6ﾓ12x 4 6ﾓ1 2x 3 6ﾓ1 3x 2 + x + 1 6ﾓ1 6ﾓ12x 4 6ﾓ1 x 3 6ﾓ1x ﾁ0803060308 03070809080309: 6ﾓ1x 3 6ﾓ1 3x 2 + 2x + 1 ｨｪ02 ﾁ07020701, 070803 07080304030207 04030009070903010206 03070809080903 ﾁ 090002 ﾁ090808. 08030508030109 0209070809040708 0809090308 010301030208, 0903050209 07080304030201 03070306030202030503 03070809080909 0309090003080705 010302010403 07080304030207 0203000708030005 q(x). ｨｹ080308 040307000302020708 03070809080309 07

138 ｨ. ｨｰ. ｨｰ0503090203 ﾁ07090708 0009020308 0307080908090301 r(x) 0308 02030003020705 p(x) 0209 q(x). 02070007 0003 040307000302020708 03070809080309 0609 ﾁ0302 02090008, 0803 0503 ﾁ03060508, 070803 040603070303040003 02030003020703 020901030003. ｨｲ09 ﾁ0306040701 0900050306070801 02030003020705 ﾁ 060907070109080607 ﾁ0903010301 04060701030603: 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 2x 3 + x 2 + 1 4x 5 + 2x 4 + 2x 2 2x 2 6ﾓ1 x 6ﾓ1 0;5 6ﾓ12x 4 6ﾓ1 2x 3 6ﾓ1 3x 2 + x + 1 6ﾓ1 6ﾓ12x 4 6ﾓ1 x 3 6ﾓ1x 6ﾓ1x 3 6ﾓ1 3x 2 + 2x + 1 6ﾓ1 6ﾓ1x 3 6ﾓ10; 5x 2 6ﾓ1 0; 5 6ﾓ12;5x 2 + 2x + 1;5 ｨｲ02030701 2x 2 6ﾓ1 x 6ﾓ1 0;5 0203040300020303 07090708020303, r(x) = 6ﾓ12;5x 2 + 2x + 1;5 03070809080309 0308 02030003020705 p(x) 0209 q(x). ｨｰ0303090001080908 02030003020705 0103000203 0309040707090801 07 080909: 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 = (2x 3 + x 2 + 1) (2x 2 6ﾓ1 x 6ﾓ1 0; 5) + (6ﾓ12; 5x 2 + 2x + 1; 5): ｨｦ0007 080909: 4x 5 6ﾓ1 2x 3 6ﾓ1 x 2 + x + 1 2x 3 + x 2 = 2x + 1 2 6ﾓ1 x 6ﾓ1 0; 5 + 6ﾓ12; 5x2 + 2x + 1; 5 2x 3 + x 2 : + 1 ｨ 00050306070801 02030003020705 縺090503000903011 7 070203050209 02090302 ﾁ090808 040609 ﾁ07000301 02030003020705 縺07080906040708 0209 070809060407081 7. ｨｹ0803 020903 ﾁ09020703 03040609 ﾁ02090203 030407070902070301 090005030607080109, 040607 ﾁ03020502020201 ﾁ020403. 7. 01030003020703 01020305030700030203 ﾁ 01030803020301 0203030406030203000502020206 090305040407010703020803 ﾁ 01030003020703 01020305030700030203 ﾁ 07 0307080908090301 0103000203 ﾁ0204030002070801 0809090003 07 04030103060108 010308030209 0203030406030203000502-020206 090305040407010703020803 ﾁ. ｨｹ080308 0103080302 040706030903 0406070103020503080705 020005 02090603000203020705 01020305030700030203 ﾁ 070007 020609050706 04090209010708, 03000009020908060706 0309020902020201 (030406030203000302020201 ﾁ 09070003 ﾁ0707) 07 ﾁ03080708 ﾁ0301. 020503 0709060203070801 04060307000008-0708060706090301 0406070103060301. 0809070801 080603000903080705 060903020300070801 p(x) = x 3 + x + 4 0209 q(x) = x 2 + x 6ﾓ1 2. ｨｦ03 08030306030102 03 02030003020707 02 ﾁ0906 01020305030700030203 ﾁ 07 0307080908090301 07000302090308, 070803 07080304030201 0709070802030503 0609 ﾁ0209 1. ｨｲ020905 0300060708 ﾁ0702 01020305030700030209 040306 ﾁ0308 07080304030207, 03090407040301 08030306030109 03 02030003020707 01020305030700030203 ﾁ 07 0307080908-090301 ﾁ 070003020908060308 0403060103: x 3 + x + 4 ﾔ (x 2 + x 6ﾓ1 2)(ax + b) + (cx + d); (4) 050203 07090708020303 ax+b 07 03070809080309 cx+d 0309040707090202 07 020303040603020300050202020107 (04030909) 0903050404070107030208090107 a; b; c; d, 09030803060203 0209000203 0209080807. 07080103080701, 070803, 0904030806030007 ﾁ 070701 ﾁ0300 ﾔ, 0102 060308030007 0403020703060902090801, 070803 02090407070902020303 0609 ﾁ03020708 ﾁ03 (4) 05 ﾁ000503080705 08030002030708 ﾁ0301, 0803 03070801 0609 ﾁ03020708 ﾁ0301, ﾁ0306020201 040607 0008000206 030209070302070506 x. 06090603000203020703 020303040603-0203000502020206 090305040407010703020803 ﾁ a; b; c; d 0103000203 ﾁ03070807 06090302020107 070403070300090107. 070407040301 0706. 080306 ﾁ0208 070403070300. ｨｰ09070906030301 070903000907 ﾁ 040609 ﾁ0308 0709070807 0609 ﾁ03020708 ﾁ09 07 040607 ﾁ03020501 0403020300020203 0700030202: x 3 + x + 4 ﾔ ax 3 + (a + b)x 2 + (6ﾓ12a + b + c)x + (6ﾓ12b + d): 0603 02 ﾁ09 01020305030700030209 08030002030708 ﾁ03020203 0609 ﾁ0202 0803050209 07 080300010903 0803050209, 0903050209 030207 0701030808 03020702090903 ﾁ0203 090305040407010703020802 040607 03020702090903 ﾁ0206 0708030403020506 x. 0806070609 ﾁ0207 ﾁ0905 090305040407010703020802 01020305030700030203 ﾁ 070003 ﾁ09 07 07040609 ﾁ09 0308 0302090909 0609 ﾁ03020708 ﾁ09 040607 03020702090903 ﾁ0206 0708030403020506 06, 0403000907090301 040607 x 3 : 1 = a; 040607 x 2 : 0 = a + b; 040607 x 1 : 1 = 6ﾓ12a + b + c; 040607 x 0 : 4 = 6ﾓ12b + d:

13ｨｪ020305030700030202 07 0302020701 02030703 ﾁ030708020201 9 ｨｦ03 05080308 07070708030102 0003050903 03040603020300070801 07070903010203 090305040407010703020802: a = 1, b = 6ﾓ11, c = 4, d = 2. 000304030601 0103000301 0209040707090801 07 060303090001080908 02030003020705: x 3 + x + 4 = (x 2 + x 6ﾓ1 2)(x 6ﾓ1 1) + 4x + 2; 050203 x 6ﾓ1 1 0203040300020303 07090708020303; 4x + 2 03070809080309 0308 02030003020705 01020305030700030209 x 3 + x + 4 0209 010203050307000302 x 2 + x 6ﾓ1 2. ﾂ0803060308 070403070300. 080302070809 ﾁ000505 ﾁ 08030002030708 ﾁ03 (4) ﾁ0103070803 04030603010302020308 x 0406030703 ﾁ030001020203 0707070009, 0009020301 0403000907090801 0609 ﾁ03020708 ﾁ09, 07030203060009060703 0203030406030203000502020203 090305040407010703020802 a; b; c; d. 070002070203 ﾁ 09090703-0708 ﾁ03 0302090703020708 x ﾁ02000706090808 0809090703, 040607 09030803060206 0009020908 04030009070908010705 0209070003000303 04060307080203 0703030802030403020705 0103000209 a; b; c; d. 07080103080701, 070803 020005 02090603000203020705 07030802060506 090305040407010703020803 ﾁ 080603000903080705 070308020603 090609 ﾁ- 0203020705. ｨｮ00030203 ﾁ09080300010203, 0209000203 ﾁ020006090801 070308020603 0302090703020705 x. ｨｲ090103080701, 070803 x = 1 07 x = 6ﾓ12 { 0903060207 09 ﾁ090206090802030503 080605060700030209 x 2 + x 6ﾓ1 2. 08030508030109 ﾁ02000706090301 070003020908060703 0302090703020705 x: 0, 1, {2, {1. 0003050209 0703 08030002030708 ﾁ09 (4) 0403000907090301: 040607 x = 0: 4 = 2b + d; 040607 x = 1: 6 = c + d; 040607 x = 6ﾓ12: 6ﾓ16 = 6ﾓ12c + d; 040607 x = 6ﾓ11: 2 = 6ﾓ12(6ﾓ1a + b) + (6ﾓ1c + d): ｨｹ0803 07070708030109 0703 07030802060506 090609 ﾁ0203020708 07 0703080206010105 02030703 ﾁ03070802020107, 040607 06030403020703 09030803060308 020300000202 04030009070708010705 0803 0003 0709010203 0302090703020705 0203030406030203000502020206 090305040407010703020803 ﾁ a = 1, b = 6ﾓ11, c = 4, d = 2. 0609 ﾁ0304060307 03 080301, 0909090308 0703 07040307030003 ﾁ 0707040300010303 ﾁ090801 0009070403, 0308 ﾁ03080701 080909: 0209000203 ﾁ000902030801 030003070107 070403070300090107 07 0203080708 ﾁ03 ﾁ090801 0403 0707080909010707. 8. 06090700030001040708 0300060708 0203000708030001 02 ﾁ0906 01020305030700030203 ﾁ 0809070801 02090202 02 ﾁ09 01020305030700030209 p(x) 07 q(x). 0700060701 020300070803000301 05080706 01020305030700030203 ﾁ 02090302 ﾁ0903080705 0809090308 010203050307000302 d(x), 09030803060208 05 ﾁ000503080705 020300070803000301 p(x) 07 q(x). 06090700030001040701 0300060701 020300070803000301 02 ﾁ0906 01020305030700030203 ﾁ p(x) 07 q(x) 02090302 ﾁ0903080705 080308 0706 0300060708 0203000708030001 D(x), 09030803060208 02030007080705 0209 0008000308 020609050308 0300060708 0203000708030001 01020305030700030203 ﾁ p(x) 07 q(x). 080607 05080301 070704030001030903080705 0300030302090703020703 D(x) = 060701(p(x); q(x)). ｨｦ03 0508030503 0304060302030003020705 07 0703 0304060302030003020705 020300070103070807 01020305030700030203 ﾁ 07000302090308, 070803: 1) 02090700030001040708 0300060708 0203000708030001 050803 080308 0300060708 0203000708030001, 09030803060208 0701030308 02090700030001040908 07080304030201; 2) 02090700030001040708 0300060708 0203000708030001 01020305030700030203 ﾁ p(x) 07 q(x) 05 ﾁ000503080705 030207020708 ﾁ0302020201 07 080307020307080108 0203 0707070003 ﾁ030503 010203000708030005, 030800070702030503 0308 02090005 (07 080307020307080108 0203 01020305030700030209 02090003 ﾁ0308 07080304030207). 0608030002 0209080807 02090700030001040708 0300060708 0203000708030001 01020305030700030203 ﾁ p(x) 07 q(x), 0103000203 060903000300070801 0706 0209 010203000708030007. 080607010306 1. 0609080807 02090700030001040708 0300060708 0203000708030001 02 ﾁ0906 01020305030700030203 ﾁ p(x) = x 3 6ﾓ1 4x 2 6ﾓ1 5x 07 q(x) = 2x 4 6ﾓ1 x 3 6ﾓ1 3x 2 : ｨｰ030403020703. ｨｰ090300030007 ﾁ 020902020203 01020305030700030202 0209 010203000708030007, 04030009070701 p(x) = x(x + 1)(x 6ﾓ1 5); q(x) = x 2 (x + 1)(2x 6ﾓ1 3): ｨｦ03 0508030503 06090300030003020705 ﾁ07020203, 070803 0302020701 0703 02090700030001040706 0300060706 020300070803000308 01020305030700030203 ﾁ p(x) 07 q(x) 070009000708 010203050307000302 D(x) = x(x + 1), 080909 090909 0302 05 ﾁ000503080705 0300060701 020300070803000301 020902020206 01020305030700030203 ﾁ, 07010308060701 02090700030001040908 07080304030201. 0506030103 02090802030202030503 0209070003000104030503 030006030503 0203000708030005 D(x), 0103000203 09090903090801 020609050308 02090700030001040708 0300060708 0203000708030001 080306 0003 01020305030700030203 ﾁ p(x) 07 q(x), 0209040607010306, D 1 (x) = 6ﾓ1x(x + 1), 070007 D 2 (x) = = 0;5x(x + 1). ﾂ0703 080607 02090700030001040706 0300060706 0203000708030005 D(x), D 1 (x), D 2 (x) 03080007070908080705 080300010903 0707070003 ﾁ020107 0102030007080300050107, 0203 0609 ﾁ02020107 02090008. 070002070203 ﾁ02000706090808 080308 02090700030001040708 0300060708 0203000708030001,

1310 ｨ. ｨｰ. ｨｰ0503090203 ﾁ07090708 090305040407010703020802 0903080306030503 ﾁ030907010203 040603070802, 0803 03070801 0203 0701030808 030006030503 0203000708030005, 030800070702030503 0308 1. ﾂ 020902020301 070009070903 D(x) = x(x + 1). 02070007 01020305030700030202 p(x) 07 q(x) 060903000300070801 0209 010203000708030007 0203 09020905080705, 0803 0706 02090700030001040708 0300060708 0203000708030001 ﾁ0703050209 0103000203 0209080807 07 04030103060108 090005030607080109 02 ﾁ0900070209 020005 01020305030700030203 ﾁ. ｨｹ080308 070403070300 09020900030507070302 090005030607080109 02 ﾁ0900070209 020005 02090603000203020705 060701 02 ﾁ0906 0209080906090001020206 0707070300 07 03070203 ﾁ0902 0209 08030306030103 03 02030003020707 02 ﾁ0906 01020305030700030203 ﾁ 07 0307080908090301. ｨ 00050306070801 02 ﾁ0900070209 020005 01020305030700030203 ﾁ p(x) 07 q(x) 0103000203 0309040707090801 ﾁ ﾁ070203 070003020908060308 01030403070907 0609 ﾁ03020708 ﾁ: p(x) = q(x)t 1 (x) + r 1 (x); q(x) = r 1 (x)t 2 (x) + r 2 (x); r 1 (x) = r 2 (x)t 3 (x) + r 3 (x);.............................. r s6ﾓ12 (x) = r s6ﾓ11 (x)t s (x) + r s (x); r s6ﾓ11 (x) = r s (x)t s+1 (x); 060701(p(x); q(x)) = r s (x). 080607010306 2. 0609080807 02090700030001040708 0300060708 0203000708030001 02 ﾁ0906 01020305030700030203 ﾁ p(x) = x 5 + x 4 + 2x 3 + 3x 2 + 2 07 q(x) = 2x 4 + 3x 3 + x 2 + 2x + 1: ｨｰ030403020703. ｨｮ080304030201 01020305030700030209 p(x) 0203 010302010403 07080304030207 01020305030700030209 q(x). ｨｰ09030203000701 p(x) 0209 q(x) 縺090503000903011 7, 040607 05080301 0102 0009020301 0703010302050801 090305040407010703020802 080909, 0708030002 ﾁ 0406030103070703 02030003020705 0203 ﾁ03030207-09090003 02060300020206 090305040407010703020803 ﾁ. ｨｹ0803 0203 030806090307080705 0209 060701, 080909 090909 0302 030406030203000503080705 07 080307020307080108 0203 0707070003 ﾁ030503 010203000708030005, 0203 0609 ﾁ02030503 02090008. ｨｦ080909, 09010203000701 ﾁ0703 090305040407010703020802 01020305030700030209 p(x) 0209 2 07 020907020501 02030003020703: 2x 5 + 2x 4 + 4x 3 + 6x 2 + 4 2x 4 + 3x 3 + x 2 + 2x + 1 2x 5 + 3x 4 + x 3 + 2x 2 + x x 6ﾓ1x 4 + 3x 3 + 4x 2 6ﾓ1 x + 4 000304030601, 0708030002 040607 02090001020308040301 02030003020707 0203 040305 ﾁ000500070701 02060300020203 090305040407010703020802, 09010203000701 ﾁ0703 0700030202 04030009070302020308 0609030203070807 6ﾓ1x 4 + 3x 3 + 4x 2 6ﾓ1 x + 4 0209 2 07 040603020300000701 02030003020703: 6ﾓ12x 4 + 6x 3 + 8x 2 6ﾓ1 2x + 8 2x 4 + 3x 3 + x 2 + 2x + 1 6ﾓ12x 4 6ﾓ1 3x 3 6ﾓ1 x 2 6ﾓ1 2x 6ﾓ1 1 6ﾓ11 9x 3 + 9x 2 + 9 ｨｪ02 0403000907070007 040306 ﾁ0208 03070809080309 r 1 (x) = 9x 3 + 9x 2 + 9. ｨｰ09030203000701 ﾁ0703 030503 090305040407010703020802 0209 9 (04030009-070302020208 ﾁ 06030309000108090803 010203050307000302 070203 ﾁ09 030003030209070701 r 1 (x)), 09 0309080301, 070704030001030905 0900050306070801 02 ﾁ0900070209, 0609030203000701 q(x) 0209 r 1 (x): 2x 4 + 3x 3 + x 2 + 2x + 1 x 3 + x 2 + 1 2x 4 + 2x 3 + 2x 2x + 1 x 3 + x 2 + 1 x 3 + x 2 + 1 0 01030003020703 0309 ﾁ030604030203, 080909 090909 040300090707000705 03070809080309, 0609 ﾁ020208 02090008. ｨｮ00030203 ﾁ09080300010203, 0703050009070203 09000503-0607080109 02 ﾁ0900070209, 040307000302020708 020302090003 ﾁ0308 03070809080309 03070801 02090700030001040708 0300060708 0203000708030001. ｨｦ080909 060701(p(x); q(x)) = x 3 + x 2 + 1. 0609040301020701, 070803 060701 030406030203000503080705 07 080307020307080108 0203 0707070003 ﾁ030503 010203000708030005, 0203 0609 ﾁ02030503 02090008. ｨｲ090103080701, 070803 03070007 03020702 0703 02 ﾁ0906 01020305030700030203 ﾁ 0609 ﾁ0302 02090008, 0803 020005 0809090308 04090602 04030205080703 060701 0203 03040603020300030203. 080607010306 3. ｨｮ0309060908070803 0206030001 x2 + 4x 6ﾓ1 5 5x 3 + 6x 6ﾓ1 11.

13ｨｪ020305030700030202 07 0302020701 02030703 ﾁ030708020201 11 ｨｰ030403020703. 060908020501 060701(x 2 + 4x 6ﾓ1 5; 5x 3 + 6x 6ﾓ1 11), ﾁ0307040300010303 ﾁ09 ﾁ04070701 09000503060708010301 02 ﾁ0900070209. ｨｦ01030301 5x 3 + 6x 6ﾓ1 11 x 2 + 4x 6ﾓ1 5 5x 3 + 20x 2 6ﾓ1 25x 5x 6ﾓ1 20 6ﾓ120x 2 + 31x 6ﾓ1 11 6ﾓ120x 2 6ﾓ1 80x + 100 111x 6ﾓ1 111 0803000907070007 040306 ﾁ0208 03070809080309 111x 6ﾓ1 111. ｨｰ09030203000701 030503 0209 111 07 040603020300000701 0900050306070801. x 2 + 4x 6ﾓ1 5 x 6ﾓ1 1 x 2 6ﾓ1 x x + 5 5x 6ﾓ1 5 5x 6ﾓ1 5 0 08030009070302 03070809080309, 0609 ﾁ020208 02090008. 01030003020703 0309 ﾁ030604030203. ｨｮ00030203 ﾁ09080300010203, 06090302030007 ﾁ 040307000302020708 03070809080309 0209 5, 04030009070701: 060701(x 2 + 4x 6ﾓ1 5; 5x 3 + 6x 6ﾓ1 11) = x 6ﾓ1 1: ｨｰ09030203000701 0209 x 6ﾓ1 1 070707000708030001 07 0302090103020908030001 0206030007 x2 + 4x 6ﾓ1 5 5x 3. ﾂ030704030001030903010705 070603010308 040306- + 6x 6ﾓ1 11 02030609 2 020005 01020305030700030209 x 2 + 4x 6ﾓ1 5. x = 1 1 4 6ﾓ15 1 5 0 ｨｲ0209070708, x 2 + 4x 6ﾓ1 5 = (x 6ﾓ1 1)(x + 5). 000304030601 040603020300090301 0803 0003 020005 01020305030700030209 5x 3 + 6x 6ﾓ1 11. x = 1 5 0 6 6ﾓ111 5 5 11 0 ｨｲ0209070708, 5x 3 + 6x 6ﾓ1 11 = (x 6ﾓ1 1)(5x 2 + 5x + 11). 000304030601 0403000907090301 x2 + 4x 6ﾓ1 5 5x 3 + 6x 6ﾓ1 11 = (x 6ﾓ1 1)(x + 5) (x 6ﾓ1 1)(5x 2 + 5x + 11) = x + 5 5x 2. 08030009070302020905 0206030001 + 5x + 11 0203 070309060908070109. ｨｰ0503090203 ﾁ07090708 ｨ 0202060308 ｨｰ090409070003 ﾁ0707, 020301030208 09090403020602 010908030109080707030709030503 09020900070309 07 0103080302070907 04060304030209 ﾁ09020705 01090803010908070907 ｨｪ03070903 ﾁ0709030503 05030603020709030503 040302090503050707030709030503 090207 ﾁ0306070708030809 (ｨｦ02070807080908 01090803010908070907 07 0702040306010908070907); 0909020207020908 0803060207070307090706 02090909, 09070708030001 01090803010908070907 ﾁ0207040308 090908030503060707, ｨｬ090906030908 040609020809 080609 ﾁ07080300010708 ﾁ09 ｨｪ030709 ﾁ02 ﾁ 0704030603 030006090303 ﾁ09020705. E-mail: riazanovskiy@mail.ru 2 ｨｮ06030109 04030602030609 09060908090708 070403070300 030904070707 090305040407010703020803 ﾁ 020304030002030503 0709070802030503 07 03070809080909 040607 02030003020707 020309030803-06030503 01020305030700030209 0209 02 ﾁ0907000302 040306 ﾁ0308 07080304030207 ﾁ070209 x 6ﾓ1 a; 03070809080309 040607 05080301 0009020308 00070003 02090003 ﾁ0201, 00070003 0102030503070003020301 02090003 ﾁ0308 07080304030207, 08.03. 020302090003 ﾁ0201 070707000301. 08060302030009080803 020307090300010903 02030003020708 09050300090301 060903000707020206 01020305030700030203 ﾁ 0209 x 6ﾓ1a, 040302090000080209080803 0309 0903050404070107030208090107 020304030002030503 0709070802030503 07 03070809080909 07 07030300060903070803, 090909 030904030002050801 08090000070109 0706030102 04030602030609.

13000607050302030103080607070307090703 01020305030700030202 02. ｨｲ. ｨｮ09 ﾁ03060103 ﾁ09 08060302000905090301 ﾁ02070109020708 070708090803000308 070809080108 0209 08030109, 09030803060308 090203000503080705 0203 080909 0900 0102030503 ﾁ02070109020705 ﾁ 0409030001020308 040603050609010103, ﾁ 080301 0707070003 07 020005 04060304070001020206 090009070703 ﾁ 080607050302030103080607-070307090703 01020305030700030202. ｨ ﾁ080306 04030700030203 ﾁ09080300010203 060903 ﾁ07 ﾁ090308 080303060708 07 040607 ﾁ03020708 0300040706020208 070407070309 0309020907, 010203050703 0703 09030803060206, 0209040607010306, 06030403020703 080607050302030103080607070307090706 090609 ﾁ0203020708 ﾁ020703090706 070803-0403020308, 0103000203 060907070109080607 ﾁ090801 090909 030902090707 0403 ﾁ02040302020308 080609020203070807 0403 030802030403020708 09 040603050609010103 04060304070001020206 090009070703 ﾁ. ｨｮ0809080105 04030709080903080705 07 040603020300000302070301. 0806030207070003 ﾁ0703 07020209000202 09 ﾁ080306 05080308 070809080107 0603040700 04030406030003 ﾁ090801 060304090801 080607050302030103080607070307090703 090609 ﾁ0203020705 090509-0202 ﾁ0902070301 090306020308 (08.03. 07020907090009 0905090202 ﾁ090801 0903060207, 09 0403080301 020309090302 ﾁ090801, 070803 020609050706 020308). ﾂ 03080007070703 0308 03000207020206 01020305030700030203 ﾁ, 03070007 060907070109080607 ﾁ090801 080607050302030103080607070307090703 01020305030700030202, 08.03. 01020305030700030202 0308 070702090709 07 0903070702090709 06, 070007, 070803 0803 0003 0709010303, 0709010102 f(x) = 09 n cos nx+b n sin nx+ + a 0, 0803, 0905090209 ﾁ 03020702 090306030201, 020304030205080203, 090909 0403020703070801 07080304030201. ｨｮ020907090009 05 020901090009, 070803 020005 0308 ﾁ030809 0209 ﾁ0303020709040703 09 01030205 ﾁ030406030702 02030708090803070203 030905000502090801 ﾁ 0909090308 020700090201 07040609 ﾁ0307020709. ｨｪ0203 09020900030701 0209080807 02030109 03020203080301020908 050201070900030403020708, 0203 080901 020707030503 0403 0508030109 0403 ﾁ030209 0203 00020003. 0003050209 05 0708090009 020901090801 07090109. ﾂ 06030309000108090803 04030009070700090701 050809 070809080105. ｨｪ0203 09090003080705, 030209 0009020308 070208030603070209 080301, 090803 02030102030503 030209090301 07 0300020702020107 010203050307000302090107. 0609040607010306, 0403 0902070503 ｨｮ. ｨｬ. 000900090702070903 ﾁ09 1. 040009 ﾁ09 1. 060803 0809090303 080607050302030103080607070307090708 010203050307000302? 000607050302030103080607070307090708 010203050307000302 (07030906090603020203 00ｨｪ) 050803 04090209010705, 09030803060908 0103000203 0403000907070801 0703 0300020702030503 01020305030700030209 0308 02 ﾁ0906 04030603010302020206 f(y; z), 030901030207 ﾁ 09 0209 cos x, 09 z 0209 sin x. 050909 030002070203, 010203050307000302 0308 0302020308 04030603010302020308 0103000203 060907070109080607 ﾁ090801 090909 07090708020208 070009070908 01020305030700030209 07 02 ﾁ090105 0403060301030202020107. 08030508030109 07090708020203 070009070907 00ｨｪ 01020305030700030202 0308 cos x (05ｨｪ) 07 01020305030700030202 0308 sin x (ｨｮｨｪ). 08060701030602 00ｨｪ: sin(x + =6); sin 2x = 2 sin x cos x. ｨｦ03 040306010900 cos(n + 1)x = cos nx cos x 6ﾓ1 sin nx sin x; sin(n + 1)x = sin nx cos x + cos nx sin x 07000302090308, 070803 040607 ﾁ070306 0209080906090001020206 n 04090209010707 cos nx 07 sin nx 00ｨｪ. ﾂ 0902070503 000900090702070903 ﾁ09 0300080507020503080705, 070803 0809090303 0708090202090608020905 0403060109 01020305030700030209. ｨｮ08090202090608-020905 0403060109 060306030409 080301, 070803 03070801 0708090202090608020905 040603010302090609 (0900050306070801) 090406030603020705 0008000308 030904070707 01020305030700030209, 09030803060905 ﾁ0703050209 040607 ﾁ03020708 09 030503 0708090202090608020308 0403060103. ｨｦ, 0209040607010306, 0708030002 090302090801, (06 + 1)(06 + 2) 07 (06 + 1) 2 + 1 030904070707 030202030503 01020305030700030209 070007 060903020206, 02030708090803070203 040607 ﾁ03070807 030009 01020305030700030209 09 0708090202090608020308 0403060103 07 070609 ﾁ02070801 06030309000108090802. 000909 090909, 0209040607010306, sin 3 x + cos 2 x sin x 07 sin x 030904070707 030202030503 07 08030503 0003 00ｨｪ, 0803 020300010305 03040603020300050801 0708090202090608020908 0403060109 00ｨｪ 090909 060303090001080908 030901030202 09 0209 cos x, 09 z 0209 sin x ﾁ 0708090202090608-020308 0403060103 01020305030700030209 0308 02 ﾁ0906 04030603010302020206. 0603 03090803 050009 ﾁ020208 04060308030202030208 0209 06030001 0708090202090608020308 0403060102 030904070701 00ｨｪ ﾁ ﾁ070203 09 n cos nx + b n sin nx + 09 n6ﾓ11 cos(n 6ﾓ1 1)x + b n6ﾓ11 sin(n 6ﾓ1 1)x + + a 1 cos x + b 1 sin x + a: 080300010309050701 040306010900090107 040603030006090303 ﾁ09020705 0406030703 ﾁ030203020708 070702090703 ﾁ 07 0903070702090703 ﾁ ﾁ 0709010102, 0103000203 040607 ﾁ03070807 09 080909030109 ﾁ070209 0008000308 00ｨｪ. 0603 04030909 09 020907 030603 020308 0203070809080307020206 03070203 ﾁ09020708 07070708090801 050809 0403060109 0708090202090608020308. ﾂ030201 0102 030603 0203 ﾁ02050702070007, 030207020708 ﾁ03020203 0007 04060302070809 ﾁ0003020703 09090002030503 00ｨｪ ﾁ 1 ｨｪ020305030700030202. 09070000070308030909 ｨｮ080904030207 030209020708", 0703060705 ｨｪ090803010908070909", ｨｪ.: 03ｨ ｨｲｨｦｨｮ, 2000. - ｨｮ.200. 12

13000607050302030103080607070307090703 01020305030700030202 13 0809090301 ﾁ070203. 0003, 070803 030207020708 ﾁ03020203070801 ﾁ02040300020503080705, 090900020208 07080902030208, 02030102030503 03020908060708 010908030109-0807070307090708 090209000703, 0003050903 02030909000308 07 04030103060108 0406030703 ﾁ0302020206. 0603 0102 0209020701 020609050303 040309070708030001020303 020309090309080300010708 ﾁ03, 070704030001030908060303 070609 ﾁ0203020703 04030607030203 ﾁ. ｨｮ0403060109000706090301 02 ﾁ09 0908 ﾁ0306000203020705: 0108 ﾁ0306000203020703 1 (03 030207020708 ﾁ03020203070807). 02070007 09 n cos nx + b n sin nx + 09 n6ﾓ11 cos(n 6ﾓ1 1)x + b n6ﾓ11 sin(n 6ﾓ1 1)x + + a 1 cos x + b 1 sin x + a ﾔ 0; 0803 a n = b n = = a = 0. 0108 ﾁ0306000203020703 2 (03 0403060703020906). 0809070801 00 03020702 0703 04030607030203 ﾁ 00ｨｪ 09 n cos nx + b n sin nx + 09 n6ﾓ11 cos(n 6ﾓ1 1)x + b n6ﾓ11 sin(n 6ﾓ1 1)x + + a 07 06030805 0002 03020702 0703 090305040407010703020803 ﾁ a i 07 b i 0203 0609 ﾁ0302 0 (i > 0). 0003050209 00 040306070302 07 020005 09 i cos ix + b i sin ix (0803 03070801 00 = (2k=i), 050203 k 0103000303 0707070003, 0308000707020303 0308 0). 0103040907080701, 070803 0102 090003 0203090903090007 0108 ﾁ0306000203020703 1. ｨｦ 0409070801 00 040306070302 020005 0803 03070801 040607 ﾁ070306 06 09 n cos nx + b n sin nx + 09 n6ﾓ11 cos(n 6ﾓ1 1)x + b n6ﾓ11 sin(n 6ﾓ1 1)x + + a; 09 n cos n(x + 00) + b n sin n(x + 00) + 09 n6ﾓ11 cos(n 6ﾓ1 1)(x + 00) + b n6ﾓ11 sin(n 6ﾓ1 1)(x + 00) + + a = = 09 n cos nx + b n sin nx + 09 n6ﾓ11 cos(n 6ﾓ1 1)x + b n6ﾓ11 sin(n 6ﾓ1 1)x + + a: 0806030300060903090301 09 i cos i(x + 00) + b i sin i(x + 00) 09 ﾁ070209 07 i cos ix + d i sin ix: 07 i cos ix + d i sin ix ﾔ 09 i (cos ix cos it 6ﾓ1 sin ix sin it) + b i (sin ix cos it + cos ix sin it) ﾔ ﾔ (09 i cos i00 + b i sin i00) cos ix + (b i cos i00 6ﾓ1 a i sin i00) sin ix: 0803000907090301, 070803 09 n cos nx + b n sin nx + 09 n6ﾓ11 cos(n 6ﾓ1 1)x + b n6ﾓ11 sin(n 6ﾓ1 1)x + + a ﾔ ﾔ 07 n cos nx + d n sin nx + c n6ﾓ11 cos(n 6ﾓ1 1)x + d n6ﾓ11 sin(n 6ﾓ1 1)x + + a: 02070007 07070708090801 0908 ﾁ0306000203020703 03 030207020708 ﾁ03020203070807 02030909030902020201, 0803 030807080209 07000302090308, 070803 040607 ﾁ070306 i ﾁ03060203 0609 ﾁ03020708 ﾁ03 a i = c i ; b i = d i, 09 030209070708, 040607 ﾁ070306 1 0308 1 0203 n 09 i cos i(x + 00) + b i sin i(x + 00) ﾔ 07 i cos ix + d i sin ix ﾔ 09 i cos ix + b i sin ix; 0803 03070801 00 040306070302 020005 09 i cos ix + b i sin ix. 000304030601 0203040907080701, 070803 0102 090003 0203090903090007 0108 ﾁ0306000203020703 2 (0203 030603 0203 0203090903090007 0108 ﾁ0306000203020703 1). ｨｦ 0409070801 0703 ﾁ0307080203, 070803 0003050209 09 n cos nx + b n sin nx + 09 n6ﾓ11 cos(n 6ﾓ1 1)x + b n6ﾓ11 sin(n 6ﾓ1 1)x + + a 1 cos x + b 1 sin x + a ﾔ 0: 09 n cos nx + b n sin nx ﾔ 6ﾓ1(09 n6ﾓ11 cos(n 6ﾓ1 1)x + b n6ﾓ11 sin(n 6ﾓ1 1)x + + a 1 cos x + b 1 sin x + a): 0603 020005 0003 ﾁ0308 0709070807 (2=n) 040306070302. ｨｲ0209070708 0703 0108 ﾁ0306000203020705 2 07000302090308, 070803 ﾁ 040609 ﾁ0308 0709070807 ﾁ0703 090305040407010703020802, 0906030103, 00020801 0103000308, 07 ﾁ0300030202030503 0700030209, 0609 ﾁ0202 0. ｨｦ02090703 (2=n) 00020003 0002 0403060703020301 020005 09 i cos ix + b i sin ix. 0803000907090301, 070803 09 n cos nx + b n sin nx ﾔ a. 0003050209 07 09 n cos 09 + b n sin 09 ﾔ 09 (080909 090909 090900020303 0707070003 09 0103000203 04060302070809 ﾁ070801 ﾁ ﾁ070203 nx). ｨｮ00030203 ﾁ09080300010203 09; a n 07 b n 08030003 0609 ﾁ0202 0.